Problem: Solve for $x$ and $y$ using substitution. ${3x+2y = 2}$ ${y = -2x-1}$
Explanation: Since $y$ has already been solved for, substitute $-2x-1$ for $y$ in the first equation. ${3x + 2}{(-2x-1)}{= 2}$ Simplify and solve for $x$ $3x-4x - 2 = 2$ $-x-2 = 2$ $-x-2{+2} = 2{+2}$ $-x = 4$ $\dfrac{-x}{{-1}} = \dfrac{4}{{-1}}$ ${x = -4}$ Now that you know ${x = -4}$ , plug it back into $\thinspace {y = -2x-1}\thinspace$ to find $y$ ${y = -2}{(-4)}{ - 1}$ $y = 8 - 1$ $y = 7$ You can also plug ${x = -4}$ into $\thinspace {3x+2y = 2}\thinspace$ and get the same answer for $y$ : ${3}{(-4)}{ + 2y = 2}$ ${y = 7}$